INTRODUCTION

Analysis of Mendelian traits is characterized by phenotypes being highly informative about the underlying genotypes (1). In contrast, analysis of complex traits is characterized by phenotypes being uninformative about the underlying genotypes (1). Complex traits are typically weakly correlated to many genes or chromosomal regions distributed across the genome. If a trait is quantitatively measured, regions of the genome containing genetic variation that influences the quantitative trait being considered are called quantitative trait loci (QTL). One limitation of linkage analysis is that its resolution is generally low, such that potentially hundreds of genes may be contained within a single QTL. Narrowing the list of positional candidate genes via comprehensive wet-lab experimentation is often prohibitively laborious and expensive.

If multiple genes correlate to the same trait, then it is reasonable to hypothesize that those genes are more likely to share one or more annotations compared with genes not correlated to that trait (2). If the hypothesis is correct, then one way to narrow a list of candidate genes resulting from a genome-wide linkage study is to search for annotations that are enriched among the candidate genes relative to randomly sampled genes and then prioritize candidate genes on the basis of those annotations. The benefit is a reduced amount of wet-lab experimentation required to identify causal genes. In the past few years, several groups have published bioinformatic methods for narrowing lists of candidate genes using a variety of gene annotations, such as gene length, expression profiles and patterns of gene duplication (3). If the hypothesis is incorrect, so long as the prioritization procedure does not result in the removal of any genes from the list or introduce misinformation, then there is minimal cost.

In this study, we used a statistical bioinformatic approach based on Gene Ontology (GO) annotation (4) to prioritize candidate genes from multiple QTL. The GO is a controlled vocabulary of terms that are organized in parent-child relationships, in which each term may have one or more parent terms. All terms ultimately descend from one of three roots: molecular function, cellular component, or biological process. These roots and their descendent child terms represent three different ways of categorizing knowledge about genes and gene products: (i) their known or predicted molecular function (e.g. type of biochemical activity), (ii) cellular locale (e.g. nucleus), or (iii) their biological role (e.g. transcription, learning and memory). A given gene, depending on the level of knowledge about it, can be annotated with terms from any of these three parts of the GO, which are also sometimes called sub-ontologies.

The GO has been used extensively in recent years as a way to mine large data sets obtained from genome-scale experiments. The typical approach has been to determine which GO terms are enriched among a given group of ‘interesting genes’, such as a list of differentially expressed genes obtained from an expression microarray experiment [see the review (5)]. Enriched GO terms serve as a description of molecular functions, cellular components, or biological processes that are most relevant to the trait under investigation.

Enrichment of GO terms for a list of genes is commonly evaluated using Fisher's exact test (5,6), which is based on the hypergeometric distribution for sampling without replacement (7). One limitation of this approach, however, is that terms are tested one at a time, ignoring the relationships between terms. As a result, subsequent corrections for multiple hypothesis testing tend to be too extreme, since tests of highly correlated terms (e.g. parents and their children) are incorrectly treated as independent. Another issue is that although the three sub-ontologies are structurally disjoint, terms both within and between sub-ontologies may be further correlated due to the fact that genes may be annotated by many terms from any of the three sub-ontologies simultaneously. To account for both sources of correlation, we developed a method that achieves dimension reduction, through principal components analysis, of the correlation structure across all GO terms in conjunction with testing for enrichment of GO terms. We then applied this method to the task of candidate gene identification and implemented a novel scoring scheme for prioritizing all candidate genes under each of any arbitrary number of QTL. We named this method Commonality of Functional Annotation (CFA). We assessed the false positive error rate and power of CFA through simulation. Finally, we applied CFA to real data sets for two quantitative, complex human traits: (i) for age-of-onset of Alzheimer's disease and (ii) for body mass index (BMI).

MATERIALS AND METHODS

Methods

Figure 1 depicts the flow of data through the CFA procedure. A collection of Python scripts, R code, data files and documentation is freely available at http://www.transvar.org/candi_gene. The details of each step are described below.

Figure 1.

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Collecting genes and GO annotations

We obtained the genomic coordinates for each marker from the primary reference or from the International HapMap Project (http://www.hapmap.org). If provided in the primary reference, we used the stated confidence intervals to determine genomic coordinates for QTL. If a confidence interval was not provided, we assumed that the interval spanned ±10 Mb centered on the marker. Assuming that 1 Mb corresponds to 1 cM, this width corresponds to a confidence interval of ±10 cM (19). This parameter is user-definable for use with any data set. We then used the UCSC Genome Informatics DAS/1 server (http://genome.ucsc.edu) [NCBI B35 assembly (20)] to retrieve GenBank accessions for mRNAs mapping to each QTL. A list of unique Entrez Gene ids corresponding to the retrieved mRNA accessions (a many-to-one mapping) was generated using the 9 May 2006 release of the gene2accession file available from the NCBI Entrez Gene ftp site (ftp://ftp.ncbi.nlm.nih.gov/gene). All GO annotations for unique Entrez Gene ids (a one-to-many mapping) were retrieved from the 9 May 2006 release of the gene2go file, also available from the NCBI Entrez Gene ftp site (ftp://ftp.ncbi.nlm.nih.gov/gene).

Constructing a genome-wide GO term correlation matrix

The gene2go file release used in this study included 5147 GO terms annotating 16 114 Homo sapiens genes. For each term, we recorded the number of unique Entrez Gene ids annotated with that term. Let f_i represent the count of genes annotated by the i-th term and let p_i = f_i / n with n = 16 114 genes. Then, for each pair of GO terms, we recorded the number of genes annotated with both of those terms. Let f_ij represent the count of genes annotated by both the i-th and j-th terms, for i ≠ j. We built a genome-wide correlation matrix R of dimensions n × n from these counts using the Pearson correlation coefficient for binomially distributed data, also known as the phi coefficient (http://www.visualstatistics.net/Visual%20Statistics%20Multimedia/crosstabulation.htm), defined as

To illustrate, consider GO:0005634 and GO:0003700, which represent the cellular component ‘nucleus’ and molecular function ‘transcription factor activity’, respectively. The number of unique Entrez Gene ids annotated with ‘nucleus’ is f₁ = 3701, the number of unique Entrez Gene ids annotated with ‘transcription factor activity’ is f₂ = 890 and the number of unique Entrez Gene ids annotated with both ‘nucleus’ and ‘transcription factor activity’ is f₁₂ = 868. Using n = 16 114, the phi coefficient between ‘nucleus’ and ‘transcription factor activity’ is r_ij = 0.429.

Additionally, conditional probabilities can be used to demonstrate that there is a relationship between terms that belong to disjoint sub-ontologies. For example, the conditional probability of a gene being annotated with ‘nucleus’, given that the gene is annotated with ‘transcription factor activity’, is pr(p₁/p₂)=0.975. Similarly, the conditional probability of a gene being annotated with ‘transcription factor activity’, given that the gene is annotated with ‘nucleus’, is pr(p₁/p₂)=0.234. Thus, there is strong correlation between these two terms even though they belong to disjoint sub-ontologies.

Testing for GO term enrichment

Consider the union of all K genes and L terms over all QTL linked to a trait. Table 3 shows the set-up for testing GO terms for enrichment. Let A represent the observed count of genes in the list annotated by a GO term. Let A + B represent the total count of genes annotated by a GO term among all genes. Let K = A + C represent the total number of genes in the list. Let A + B + C + D represent the total number of genes, which is also given by n = 16 114. Enrichment for the GO term was determined using a one-tailed Fisher's exact test.

Table 3.

2 × 2 Table for Fisher's exact test for enrichment of a Gene Ontology term

	Gene in list	Gene not in list	Total
Gene annotated with term	A	B	A + B
Gene not annotated with term	C	D	C + D
Total	A + C	B + D	A + B + C + D

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Adjusting for multiple, correlated tests

A popular method for controlling the false positive error rate among m independent tests is the full Bonferroni correction, which involves decreasing the per comparison significance level from α to α/m. If the tests are correlated, then a partial Bonferroni correction is more appropriate, with the correction being some value smaller than m. Since tests of GO term enrichment are correlated, a partial Bonferroni correction is more appropriate than a full Bonferroni correction.

To determine an appropriate correction factor for multiple tests in the presence of correlation, we first partitioned the genome-wide correlation matrix as

in which R₁ is an L × L block corresponding to the L observed GO terms relevant to the data set being analyzed. Then, we performed Velicer's minimum average partial (MAP) test on R₁ to estimate the number of principal components that should be retained (21,22). Briefly, Velicer's MAP test involves partialling out principal components from the correlation matrix and computing the average squared partial correlation (22). The number of retained principal components minimizes the average squared partial correlation (22). Since each principal component is associated with one eigenvector, and eigenvectors are orthogonal, we equated the number of retained principal components to the effective number of independent tests and all P-values were multiplied by this value. If all principal components were retained, then the partial and full Bonferroni corrections were identical. If only some principal components were retained, then the partial Bonferroni correction was smaller than the full Bonferroni correction, allowing for more rejections and retaining more power. The criterion for declaring a test for enrichment significant was that the adjusted P-value be <0.05.

Scoring genes

Let M represent a binary incidence matrix of k=1,2, …, K rows (genes) and l = 1,2,…,L columns (GO terms). Values in the incidence matrix are

Let P represent the L × L matrix of orthonormalized eigenvectors calculated from the L × L correlation matrix R₁. Eigenvectors are used to model the correlation among GO terms so that redundant information represented by correlated GO terms is not double-counted in the score for a given gene. Let w represent a L × 1 vector of weights, in which weights were assigned to each term by counting the number of QTL in which that term annotated at least one gene. A K × 1 vector of weighted scores was calculated as s=MPw. For the list of genes under a QTL, scores were ranked and the top ranked gene (or genes, in the case of ties) was considered to be the prioritized candidate gene for that QTL. This weighting scheme yields higher scores for enriched GO terms associated with multiple QTL. This scheme is based on the assumption that the recurrence of a significantly enriched GO term, with respect to multiple QTL, increases our belief that concluding significant enrichment for that particular GO term reflects a true positive result.

Assessment of the false positive error rate

To assess the false positive error rate for GO term enrichment, we simulated data under the null hypothesis that a GO term annotates genes contained in the QTL as often as it annotates genes not in the QTL. To randomly generate a QTL, we randomly sampled a genomic position, using probabilities proportional to chromosome length, and defined the QTL as the interval covering 20 Mb centered on that position. The false positive error rate was defined as the percent of GO terms that were determined to be significantly enriched. We simulated data sets of two sizes, one containing three non-overlapping QTL and one containing six non-overlapping QTL. For both sizes, we generated 100 independent replicates (i.e. data sets).

Assessment of power

To assess power, we simulated data under the alternative hypothesis. Under the alternative hypothesis, a GO term annotates genes in the QTL more often that it annotates genes not in the QTL. To simulate data under this alternative hypothesis, we randomly sampled a GO term that annotated at least as many genes as QTL we were simulating and then randomly sampled genes annotated by that term. These genes were treated as quantitative trait genes and were used to seed the QTL. We then defined a QTL as the interval containing 20 Mb centered on the quantitative trait gene. We simulated data sets of two sizes, one containing three non-overlapping QTL and one containing six non-overlapping QTL. For both sizes, we generated 100 independent replicates. We defined power as the percent of replicates for which the true GO term was determined to be significantly enriched at an experiment-wide significance level α = 5.0%.

Fold-enrichment

Consider a QTL containing N total genes. In the absence of any information with which to prioritize genes within the QTL, genes can be arbitrarily ranked from 1 (highest) to N (lowest). Let u_g represent the rank of the g-th gene, g = 1,2,…,N. The average rank for a gene is = (N + 1) / 2. In the presence of information with which to prioritize genes within the QTL, causal genes should move toward the top of the list. We defined fold-enrichment (FE) for the g-th gene in the QTL as the average rank of a gene before prioritization divided by the rank of the g-th gene after prioritization,

Plausibility analysis

Some GO terms that CFA identified as significantly enriched for a particular data set may have been previously associated with the relevant phenotype. To test the biological plausibility of the GO terms identified as significantly enriched, we assessed the co-occurrence of those terms in both the Entrez Gene and Online Mendelian Inheritance in Man (OMIM, http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=OMIM) databases. First, we searched the current records in Entrez Gene using the phenotype, GO term and organism. An example of such a query was ‘Alzheimer's and “membrane” [GO] and Homo sapiens’. We recorded all unique genes returned by this query. We repeated this search using all significantly enriched GO terms for a phenotype and compiled all genes into a single list. For each gene in this list, we reviewed its corresponding record in OMIM and searched for the occurrence of the relevant phenotype in the gene's description. The proportion of genes in OMIM associated with the phenotype among the genes in Entrez Gene also associated with the phenotype provides a measure of consistency across the two databases.

RESULTS

DISCUSSION

In this study, we describe CFA, a method for prioritizing candidate genes from genome-wide linkage studies. The fundamental assumption of the method is that genes linked to a complex trait are more likely to share annotation (such as GO annotation) than genes chosen at random, such that some shared annotations will be enriched among genes linked to the trait. Of 163 genes involved in 29 diseases for which at least three genes are reported to affect risk, 80% shared an annotation with another gene for the same disease (29). Researchers have taken advantage of this enrichment to identify genes involved in breast cancer (30). Ritchie et al. (31) identified four SNPs in three genes from the estrogen metabolism pathway that are strongly associated with sporadic breast cancer. Pathway information has been used to identify candidate genes in expression-based studies for autism (32) and prostate cancer (33). Recently, a follow-up study to the identification of the involvement of complement factor H in age-related macular degeneration (34) identified several SNPs in the complement pathway, indicating that other genes in the complement pathway besides factor H may be involved in this disease (35). On the other hand, it is possible that complex traits are characterized by genetic heterogeneity such that annotations are not enriched among genes correlated to the same trait. For such traits, CFA is a valid statistical procedure in the sense that the false positive error rate is properly controlled, but will have no power to detect true positives.

CFA utilizes principal components analysis to account for the correlation structure both within and between the three GO sub-ontologies. Furthermore, since the genome-wide correlation matrix is constructed by considering all possible pairs of terms, CFA is completely independent of the location of terms within the GO hierarchy, allowing terms to be compared regardless of their generality. We test for enrichment of GO terms using Fisher's exact test. We stress that the unit of testing is a GO term and not a gene. Principal components analysis further allows for dimension reduction, thereby mitigating multiple testing. As the GO hierarchy acquires more terms and the level of annotation of human gene products deepen, the problems related to multiple hypothesis testing will become more severe, thus increasing the need for estimating the true number of independent tests using the PCA approach presented here. As an additional benefit, the principal components analysis can be used in conjunction with any term-by-term test, not just Fisher's exact test. We develop a scoring function in which a gene score is determined by the presence or absence of annotation by significantly enriched GO terms for that gene. Genes annotated with more significantly enriched GO terms have higher scores. Genes can be prioritized by ranking them on the basis of their scores in descending order, such that genes with higher scores receive higher priority. We tested CFA using simulated data and found that it was conservative (in our opinion, acceptably so for an exploratory, data-mining task), but had good power. We used this method to prioritize candidate genes for QTL linked to two complex traits, Alzheimer's disease and BMI (Tables S1 and S3, respectively).

To our knowledge, CFA is the first method to use principal components analysis to account for the correlation structure among all GO terms. In concept, this approach is similar to the use of principal components analysis of gene expression data for groups of genes (36–38). The correlation structure among GO terms affects analysis in two ways: (i) tests for enrichment for individual GO terms are dependent and (ii) weights for GO terms in the gene scores are correlated. Several methods have been developed that account for dependencies within sub-ontologies but do not (as yet) account for dependencies between sub-ontologies (39–43). For gene expression data, Delongchamp et al. (44) developed a meta-analytic method to combine P-values that accounts for the correlation of P-values within a group of genes defined by a single GO term but does not account for correlation among groups. Several groups have developed resampling-based procedures to assess significance (37,45). Permutation testing and bootstrapping of gene expression data do not require estimation of the correlation structure but are computationally expensive. Pinto et al. (46) used bootstrapping to assess significance of correlation coefficients between distance measures for gene expression and annotation measures. Our use of Velicer's MAP test to achieve dimension reduction and the use of this dimension reduction to mitigate multiple testing appears to be novel. Velicer's MAP test has a statistically justified basis and does not require subjective thresholding in terms of the proportion of variance explained when determining the number of principal components to retain (22).

Bioinformatic methods for identifying candidate genes employing GO annotation include SUSPECTS (47,48), G2D (49,50) and POCUS (29). Of these methods, CFA is most similar to POCUS. In contrast to SUSPECTS and G2D, POCUS and CFA do not require training sets. A critical limitation of training sets is that only candidate genes sharing annotation with training genes can be detected; true candidate genes not sharing annotation with training genes cannot be detected. POCUS bases it score on the frequency with which genes from more than one locus share a given annotation. POCUS's power was estimated to be 65% for data sets containing an average of 20 genes, 19% for data sets containing an average of 94 genes and 15% for data sets containing an average of 187 genes (29). In comparison, CFA's power was estimated to be 71% for data sets containing three loci of ∼130 genes each and 78% for data sets containing six loci of ∼137 genes each. Whereas POCUS loses power as the size of the data set increases, CFA gains power. A full Bonferroni correction is more conservative than a partial Bonferroni correction, and this difference increases with larger data sets. By accounting for correlations among GO terms, a partial Bonferroni correction based on principal components analysis of the correlation matrix effectively preserves power for larger data sets. Furthermore, for similarly sized data sets, CFA appears to be substantially more powerful than POCUS. POCUS requires more than one susceptibility locus; CFA works with any number of susceptibility loci. POCUS further assumes sharing events (i.e. GO terms) are independent; CFA explicitly accounts for two sources of correlation among GO terms.

We applied the CFA method to the results from studies investigating the genetic basis of two different quantitative traits: BMI and age-of-onset for Alzheimer's disease. Our analyses revealed several previously known candidate genes and proposed several new candidate genes influencing these traits. However, our findings may represent false positives, and we give five reasons for why this might be the correct explanation. First, QTL reported in the original studies might be false positives. Our simulation demonstrated that CFA retained validity in the absence of true positive QTL, so this possibility is unlikely. Second, genes may be incorrectly located on the current assembly of the human genome. Third, given the low resolution of linkage studies, a region of 20 Mb centered on the nearest significant marker may have missed the true linked gene(s). Given that significant linkage indicates either QTL with small effects close to the marker or QTL with large effects distant from the marker, and given that complex traits generally involve many loci with small effects, we believe this possibility to be unlikely. Fourth, the annotation of genes in GO is incomplete and biased toward highly studied genes; thus, novel or poorly characterized genes could be missed. Fifth, significantly small P-values from Fisher's exact test might represent false positives, even after correcting for multiple tests. Our simulation indicated that power to detect true patterns of enriched GO terms is >70%, strongly suggesting that the candidate genes reported here may represent true positives.

A recurrent finding of CFA is that significant enrichment of GO terms appears to result from linkage of genes from the same family arising from gene duplication. Duplication can give rise to genes in the same QTL that are more likely to share annotations than are unrelated genes. If one QTL contains many such duplicates, the associated annotations may remain significantly enriched even when combined across multiple QTL. This phenomenon may apply to the antigen presentation genes and odorant receptor genes for Alzheimer's disease and the cadherin superfamily genes forBMI. In the former two cases, relevant GO terms annotated genes in only one QTL, and we may be more inclined to believe that significant enrichment resulted solely from gene duplication. In contrast, in the latter case, cell adhesion GO terms annotated genes in 16 of 18 QTL, with QTL derived from multiple studies, and we may be more inclined to believe that significant enrichment resulted from true commonality. A possible implication of these findings is that QTL for complex traits may tend to contain gene duplicates, such that the duplication may be a predictive correlate to disease susceptibility (51).

Candidate genes associated with Alzheimer's disease have been identified for the QTL at 11q25 (SORL1) (23) and 14q22 (PSEN1) (24,25). No clear identification of candidate genes exists for the QTL at 6q27. Based on our results, we hypothesize that candidate genes at this QTL may affect age-on-onset via MHC class I antigen presentation. Interestingly, ULBP expression renders cells sensitive to cytotoxicity mediated by natural killer cells and is blocked by human cytomegalovirus glycoprotein UL16 (52). At this time, it is unclear if this process reflects infection, possibly with a herpesvirus (53), or an autoimmunity-related phenomenon.

For the BMI data, none of the top-scoring genes has been previously associated with this quantitative trait. We observed two potentially meaningful groupings of significantly enriched GO terms. One group annotated transcription factors and the other group annotated cell adhesion molecules. Cell adhesion is the biological process defined as ‘the attachment of a cell, either to another cell or to an underlying substrate such as the extracellular matrix, via cell adhesion molecules’ (http://www.godatabase.org). For these GO terms, several of the top-scoring genes are members of the cadherin superfamily. According to Entrez Gene, cadherin superfamily genes, such as PCDH17, PCDH20, CDH22 and PCDHB7, are speculated to affect cell–cell neural connections. Based on our results, we hypothesize that there may be an association between BMI and genes in the cadherin superfamily. In support of this hypothesis, the cadherin gene fat was recently found to affect organ size in Drosophila (54).

There are many possible extensions to this work. First, more linkage studies could be examined, and a scheme that weights for replicability of QTL across studies could be devised. Second, GO annotations are accompanied by evidence codes that also have a hierarchical structure of reliability. A weighting scheme that incorporates this information could be devised [for one example see (55)]. Third, tests for composite annotation could be investigated (56). Fourth, additional sources of information such as gene expression, protein–protein interaction networks, tissue specificity, KEGG or BioCarta pathways and sequence homology, could be integrated into a combined statistic in a manner similar to Maestro (57) or Endeavour (58). For these types of integrative methods, it is critical to account for the covariance of the different data sources. Principal components analysis provides a way to account for covariance while also allowing for dimension reduction. Fifth, biological confirmation of the candidate genes should be performed. Sixth, more powerful methods of correcting for multiple tests could be implemented (59). Interestingly, for both real data analyses, the partial Bonferroni correction and the Benjamini–Hochberg false discovery rate yield the same number of rejected null hypotheses (data not shown), suggesting that these two post hoc methods are comparably powerful. Seventh, by taking advantage of extensive GO annotations available for multiple species, we have generated genome-wide GO term correlation matrices for Arabidopsis thaliana, Drosophila melanogaster, Mus musculus and Saccharomyces cerevisiae. Thus, CFA can be readily applied to linkage data from these model organisms.

Taken together, our work has generated a promising new set of candidate genes that may assist in defining genetic factors linked to Alzheimer's disease and BMI. If confirmed, these genes may offer new targets for diagnosis and treatment. More broadly, CFA can generate a prioritized set of candidate genes that may assist in defining genes linked to complex traits.

SUPPLEMENTARY DATA

Supplementary Data are available at NAR Online.